The Nielsen reduction and P-complete problems in free groups
Theoretical Computer Science
A taxonomy of problems with fast parallel algorithms
Information and Control
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The set of minimal braids is Co-NP-complete
Journal of Algorithms
Handbook of theoretical computer science (vol. B)
Word Problems Solvable in Logspace
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
On simultaneous resource bounds
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Decidability and complexity in automatic monoids
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Logspace computations in graph groups and coxeter groups
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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Hyperbolic groups are a rich class of groups frequently encountered in mathematical research, particularly in topology. It has been the focus of intense study by many combinatorial group theorists and topologists recently. We present some computational results for infinite groups, especially for hyperbolic groups. It is shown that the word problem for hyperbolic groups is solvable in NC2. This is the first NC algorithm for a class of groups in combinatorial group theory. We also consider the isomorphism problem of randomly generated groups using a novel technique: the Alexander polynomial from knot theory. These randomly generated groups are almost always hyperbolic groups.